VPN is a specialized proxy in that it allows you to connect to some network which then does your requests on your behalf. VPN has significant advantages over a simple web proxy server (the general idea that you have greater control over network policies and how network traffic is handled).

The network map looks like it would as a man-in-the-middle attack however the man in the middle is either a machine you control (meaning you're both the client and the man in the middle) or someone you trust.